Analysis is given for flow regimes in the riser of a circulating fluidised bed (CFB) in the range of gas velocities (2-8 m/s) and particulate solids fluxes (15-90 kg/m(2) s) appropriate for a CFB combustor. It is shown that the simplest version of the core-annulus model gives the correct magnitudes of slip velocity and average solids hold-up. The anomaly in the core-annulus model, whereby diffusion of particles is towards the region of high solids concentration, is ascribed to the presence of clusters, diffusion towards the wall occurring in the dilute regions between clusters. The clusters are conjectured to be fragments of the relatively dense particle film falling near the wall: this film is shown to have features in common with a film of ordinary liquid flowing down a vertical surface. Implications for scale-up are discussed, using published data showing that very large CFBs exhibit core-annulus flow.